com.joptimizer.functions

Class LogarithmicBarrier

java.lang.Object

com.joptimizer.functions.LogarithmicBarrier

All Implemented Interfaces:

BarrierFunction, TwiceDifferentiableMultivariateRealFunction

public class LogarithmicBarrier
extends java.lang.Object
implements BarrierFunction

Default barrier function for the barrier method algorithm.
If f_i(x) are the inequalities of the problem, theh we have:
Φ = - Sum_i[log(-f_i(x))]

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, 11.2.1"

Constructor Summary

Constructors

Constructor and Description
LogarithmicBarrier(ConvexMultivariateRealFunction[] fi, int dim) Create the logarithmic barrier function.

Method Summary

Modifier and Type	Method and Description
double	calculatePhase1InitialFeasiblePoint(double[] originalNotFeasiblePoint, double tolerance) Calculates the initial value for the s parameter in Phase I.
BarrierFunction	createPhase1BarrierFunction() Create the barrier function for the Phase I.
int	getDim() Dimension of the function argument.
double	getDualityGap(double t) Calculates the duality gap for a barrier method build with this barrier function.
double[]	gradient(double[] X) Function gradient at point X.
double[][]	hessian(double[] X) Function hessian at point X.
double	value(double[] X) Evaluation of the function at point X.

Methods inherited from class java.lang.Object

equals, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Constructor Detail

LogarithmicBarrier

public LogarithmicBarrier(ConvexMultivariateRealFunction[] fi,
                          int dim)

Create the logarithmic barrier function.

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, 11.2.1"

Method Detail

value

public double value(double[] X)

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Evaluation of the function at point X.

Specified by:

value in interface TwiceDifferentiableMultivariateRealFunction

gradient

public double[] gradient(double[] X)

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Function gradient at point X.

Specified by:

gradient in interface TwiceDifferentiableMultivariateRealFunction

hessian

public double[][] hessian(double[] X)

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Function hessian at point X.

Specified by:

hessian in interface TwiceDifferentiableMultivariateRealFunction

getDim

public int getDim()

Description copied from interface: TwiceDifferentiableMultivariateRealFunction

Dimension of the function argument.

Specified by:

getDim in interface TwiceDifferentiableMultivariateRealFunction

getDualityGap

public double getDualityGap(double t)

Description copied from interface: BarrierFunction

Calculates the duality gap for a barrier method build with this barrier function.

Specified by:

getDualityGap in interface BarrierFunction

createPhase1BarrierFunction

public BarrierFunction createPhase1BarrierFunction()

Create the barrier function for the Phase I. It is a LogarithmicBarrier for the constraints:
fi(X)-s, i=1,...,n

Specified by:

createPhase1BarrierFunction in interface BarrierFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, 11.4.1"

calculatePhase1InitialFeasiblePoint

public double calculatePhase1InitialFeasiblePoint(double[] originalNotFeasiblePoint,
                                                  double tolerance)

Calculates the initial value for the s parameter in Phase I. Return s = max(fi(x))

Specified by:

calculatePhase1InitialFeasiblePoint in interface BarrierFunction

See Also:

"S.Boyd and L.Vandenberghe, Convex Optimization, 11.6.2"